In article <email@example.com>, WM <firstname.lastname@example.org> wrote: > Am Donnerstag, 6. Februar 2014 00:19:51 UTC+1 schrieb Ben Bacarisse: > > The properties of a path defined by a > > supposed bijection can be argued about perfectly well.
> If the path can be named.
WM has this thing about having to name everything. Nut he's SOL because in real mathematics there are more things than names. For example. In a Complete Infinite Binary Tree ther are more paths than WM can find names for them.
> > What exactly is the "contrary"? > The contrary is that Cantor's argument exclusively is based upon digits at > finite positions.
On the contrary, Cantor's argument was not about digits at all but about infinite strings of the letters 'm' and 'w'.
> A rational-complete list covers all these positions.
Claimed but not proved and not provable anywhere outside of WMytheology,
> And > there are no digits at infinite positions
But there can be digits at infinitely many different finite postions, which scuttles WM's arguments entirely.
> > > That's what we call an antinomy. It is a well-known paradox > > >that matheologians cannot see the other side. > > Well it would be a problem except that the contrary is not true.
> But it is true. A rationals-complete list contains all digit sequences that > can be subject to the diagonal argument
Nonsense! The finitely defined real number r = Sum_(n in |N) 1/2^(n!), in base 2, is not anywhere in WM's "rationals-complete list" or in his pseudo-binary tree, but does represent a path in any Complete Infinite Binary Tree outside of WMytheology. . --